MinT - Information on Result #1841667

Information on Result #1841667

(49, 82, 1025)-net in base 64, using net defined by OOA based on OOA(64⁸², 1025, S₆₄, 33, 33), using

OOA 16-folding and stacking with additional row [i] based on OA(64⁸², 16401, S₆₄, 33), using
- discarding factors based on OA(64⁸², 16402, S₆₄, 33), using
  - discarding parts of the base [i] based on linear OA(128⁷⁰, 16402, F₁₂₈, 33) (dual of [16402, 16332, 34]-code), using
    - constructionÂ X applied to C([0,16]) âŠ‚ C([0,13]) [i] based on
      1. linear OA(128⁶⁵, 16385, F₁₂₈, 33) (dual of [16385, 16320, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
      2. linear OA(128⁵³, 16385, F₁₂₈, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      3. linear OA(128⁵, 17, F₁₂₈, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
        discarding factors / shortening the dual code based on linear OA(128⁵, 128, F₁₂₈, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
        Reedâ€“Solomon code RS(123,128) [i]

Mode: Constructive.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	(50, 82, 1025)-net in base 64	[i]		t-Expansion
2	(50, 83, 1025)-net in base 64	[i]		Net Duplication
3	(49, 81, 1025)-net in base 64	[i]		m-Reduction